On the uniform nonsingularity of matrices of search directions and the rate of convergence in minimization algorithms

Philippe Toint; Frank Callier

doi:10.1007/BF00933294

On the uniform nonsingularity of matrices of search directions and the rate of convergence in minimization algorithms

Résultats de recherche: Contribution à un journal/une revue › Article › Revue par des pairs

Résumé

A convergent minimization algorithm made up of repetitive line searches is considered in ℝ. It is shown that the uniform nonsingularity of the matrices consisting of n successive normalized search directions guarantees a speed of convergence which is at least n-step Q-linear. Consequences are given for multistep methods, including Powell's 1964 procedure for function minimization without calculating derivatives as well as Zangwill's modifications of this procedure. © 1977 Plenum Publishing Corporation.

langue originale	Anglais
Pages (de - à)	511-529
Nombre de pages	19
journal	Journal of Optimization Theory and Applications.
Volume	23
Numéro de publication	4
Les DOIs	https://doi.org/10.1007/BF00933294
Etat de la publication	Publié - 1 déc. 1977

Accès au document

10.1007/BF00933294

Autres fichiers et liens

Link to publication in Scopus

1 Actif

ADALGOPT: ADALGOPT - Algorithmes avancés en optimisation non-linéaire
SARTENAER, A. & TOINT, P.
1/01/87 → …
Projet: Axe de recherche

Contient cette citation

@article{a5141bcc5dad49378b9abb8a088c7cbb,

title = "On the uniform nonsingularity of matrices of search directions and the rate of convergence in minimization algorithms",

abstract = "A convergent minimization algorithm made up of repetitive line searches is considered in ℝ. It is shown that the uniform nonsingularity of the matrices consisting of n successive normalized search directions guarantees a speed of convergence which is at least n-step Q-linear. Consequences are given for multistep methods, including Powell's 1964 procedure for function minimization without calculating derivatives as well as Zangwill's modifications of this procedure. {\textcopyright} 1977 Plenum Publishing Corporation.",

author = "Philippe Toint and Frank Callier",

year = "1977",

month = dec,

day = "1",

doi = "10.1007/BF00933294",

language = "English",

volume = "23",

pages = "511--529",

journal = "Journal of Optimization Theory and Applications.",

issn = "0022-3239",

publisher = "Springer New York",

number = "4",

}

TY - JOUR

T1 - On the uniform nonsingularity of matrices of search directions and the rate of convergence in minimization algorithms

AU - Toint, Philippe

AU - Callier, Frank

PY - 1977/12/1

Y1 - 1977/12/1

N2 - A convergent minimization algorithm made up of repetitive line searches is considered in ℝ. It is shown that the uniform nonsingularity of the matrices consisting of n successive normalized search directions guarantees a speed of convergence which is at least n-step Q-linear. Consequences are given for multistep methods, including Powell's 1964 procedure for function minimization without calculating derivatives as well as Zangwill's modifications of this procedure. © 1977 Plenum Publishing Corporation.

AB - A convergent minimization algorithm made up of repetitive line searches is considered in ℝ. It is shown that the uniform nonsingularity of the matrices consisting of n successive normalized search directions guarantees a speed of convergence which is at least n-step Q-linear. Consequences are given for multistep methods, including Powell's 1964 procedure for function minimization without calculating derivatives as well as Zangwill's modifications of this procedure. © 1977 Plenum Publishing Corporation.

UR - http://www.scopus.com/inward/record.url?scp=34250302505&partnerID=8YFLogxK

U2 - 10.1007/BF00933294

DO - 10.1007/BF00933294

M3 - Article

VL - 23

SP - 511

EP - 529

JO - Journal of Optimization Theory and Applications.

JF - Journal of Optimization Theory and Applications.

SN - 0022-3239

IS - 4

ER -

On the uniform nonsingularity of matrices of search directions and the rate of convergence in minimization algorithms

Résumé

Accès au document

Autres fichiers et liens

Empreinte digitale

Projets

ADALGOPT: ADALGOPT - Algorithmes avancés en optimisation non-linéaire

Contient cette citation